This invention relates to a method and apparatus for image transformation and, more particularly, to a method and apparatus employing image memories for geometrical transformation of an input image.
In general, special effect or animation forming equipment requires an image transforming apparatus for rotating, enlarging, reducing, and geometrically transforming an original image. The image transforming apparatus divides the original image into a plurality of original minute rectangular segments each including a plurality of sampling points positioned on a discrete X-Y rectangular coordinate system. Each of the original minute rectangular segments is represented by a predetermined point positioned in the corresponding original minute rectangular segment. The new position to which the representative point is to be transformed on a discrete U-V coordinate system is calculated from a transformation equation. Following this, the new position of the representative point is used to determine the new minute rectangular segment corresponding to the original minute rectangular segment from the transformation equipment. Subsequently, the inverse function of the transformation equation is used to obtain the positions of the sampling points in the original minute rectangular segment corresponding to the respective sampling points in the new minute rectangular segment. The original image is transformed into an output image by regarding the image information of the sampling points in the original minute rectangular segment as the image information of the corresponding sampling points in the new minute rectangular segment.
When the new minute rectangular segments are approximated by a parallelogram transformed in accordance with another transformation equation, the possibility exists that an empty space may be produced between adjacent new minute rectangular segments. In order to avoid this problem, it is the conventional practice to multiply a correction coefficient greater than 1 during the process for obtaining the new minute rectangular segment corresponding to the original minute rectangular segment. For example, Japanese Patent Kokai No. 60-59474 discloses an image transforming method where an input image is divided into a plurality of original minute rectangular segments in such a manner that adjacent original minute rectangular segments share a common portion. Since the new minute rectangular segment is approximated by a parallelogram, however, great errors are introduced which cause image quality deterioration.
When the position of a sampling point in the new minute rectangular segment corresponds to a position on the original minute rectangular segment between two sampling points, linear interpolation is used to obtain the image information of the sampling point in the new minute rectangular segment from the image information of some sampling points in the original minute rectangular segment. However, the value of the image information does not change linearly between sampling points in practice, causing a deviation from the actual image data.
In addition, it is the conventional practice to pass the input image information through longitudinal and lateral filtering devices in order to eliminate aliasing produced in the course of transformation of the input image. However, the filtering devices cannot prevent image quality deterioration when the image is transformed slantingly.
When the input image is transformed to be projected on a three-dimensional body such as a sphere, a cylinder, or other polyhedral bodies, the new minute rectangular segment would be divided into two portions projected on the visible and hidden surfaces of the three-dimensional curved surface near the contour between the visible and hidden surfaces. In this case, the image display is deteriorated on the contour.